Where is the vertex weight panel in 2.77
For the vertex weights panel (not to be confused with the vertex groups panel) to appear, you need to be in vertex select mode in edit mode and have a vertex that is associated with one or more vertex groups as the active selection. It should then appear on the 'N' panel.

For more info for others (the question quotes the manual):
https://www.blender.org/manual/modeling/meshes/vertex_groups/weight_edit.html